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1.Description of correlations in mean-field and beyond mean-field methods

1.Description of correlations in mean-field and beyond mean-field methods. Variational multiparticle-multihole configuration mixing method N.Pillet (1) , J.-F.Berger (1) , E.Caurier (2) , H.Goutte (1) , N.Vinh Mau (3) , F.Chappert (1). Spatial structure of Cooper pairs in HFB approach

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1.Description of correlations in mean-field and beyond mean-field methods

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  1. 1.Description of correlations in mean-field and beyond mean-field methods Variational multiparticle-multihole configuration mixing method N.Pillet(1), J.-F.Berger(1), E.Caurier(2), H.Goutte(1), N.Vinh Mau(3), F.Chappert(1) Spatial structure of Cooper pairs in HFB approach N.Pillet(1), N.Sandulescu(4), P.Schuck(3) 2.Nuclear excitations in plasmas G.Gosselin(1), V.Méot(1), N.Pillet(1) (1) SPN,CEA-Bruyères-le-Châtel (3) IPN, Orsay (2)IPHC, Strasbourg (4) IPNE, Bucharest nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  2. Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing • Motivations: • Towards a unified description of correlations in the context of beyond mean- • field method {essentially Pairing + RPA + particle-vibration coupling} • Conservation of particle numbers + enforced Pauli principle • Description on the same footing of even-even, odd and odd-odd nuclei • Description of both ground states and excited states nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  3. with and + + + … Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing method Formalism: • Trial wave function:Superposition of Slater determinants corresponding to mpmh excitations built upon a given state of HF type nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  4. Functional: Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing method • Variational principle with • Mixing coefficients: • Optimized single particle states: • Simultaneous solution of both equations (iterative): • self-consistent procedure and renormalization of the HF field nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  5. Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing method Current study: Pairing correlations and link with projection on particle number methods-Applications to Sn isotope ground states(*) Correlation energy (MeV) Only configurations with excited pairs Structure of correlated wave functions D1S Gogny force (*) N.Pillet, J-F.Berger and E.Caurier, under submission to PRC. N.Pillet, N.Sandulescu, Nguyen Van Giai and J-F.Berger, Phys.Rev.C71, 044306 (2005). nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  6. Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing method Effect of correlations on single particle spectra Charge radii nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  7. Description of correlations in mean field and beyond mean field methods Variational multiparticle-multihole configuration mixing method • Future studies: • Link with RPA – How to simulate RPA calculation with mp-mh method? • Which one-body density should be used? • Description of light exotic nuclei (B, Li, Be, C, N, O, F) – PhD Proposal • Application of the mp-mh method to odd and odd-odd nuclei • Effect of general correlations on single particle spectra • Applications to island of inversion • Re-fit of Gogny interaction (D2)? • Need for experimental data on masses, spins, parities… towards drip lines nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  8. Description of correlations in mean field and beyond mean field methods Spatial structure of Cooper pairs in HFB approach • Method:HFB with D1S Gogny interaction Two-body correlated wave function(J=0): Brody-Moshinsky transformation K(R,r) (R: center of mass, r: relative coordinates) and • Spherical nuclei:O, Ca, Ni, Sn, Pb isotopic chains (*) N. Pillet, N. Sandulescu and P. Schuck, Phys. Rev. C76, 024310 (2007). nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  9. Description of correlations in mean field and beyond mean field methods Spatial structure of Cooper pairs in HFB approach Size of Cooper pairs: Strong coupling behavior of Cooper pairs on the surface of superfluid nuclei nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  10. Description of correlations in mean field and beyond mean field methods Spatial structure of Cooper pairs in HFB approach Probability Distribution Future study: Generalization to deformed nuclei where the parity mixing is expected to be stronger + nucleon pair transfer nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  11. Nuclear excitations in plasmas Main excitation processes Photon absorption Inelastic electron scattering NEET (nuclear excitation by electronic transition) NEEC (nuclear excitation by electron capture) Corresponding de-excitation processes BIC (bound internal conversion) IC (internal conversion) Photon emission spontaneous+ stimulated nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  12. Nuclear excitations in plasmas Method for transition rate calculation: • Photon absorption, NEET and NEEC mechanisms (*): • First order perturbation theory Fermi golden rule • Inelastic electron scattering: (under development) • Second order perturbation theory • PWBA, WKB, DWBA (radial transition matrix element) (*) G. Gosselin, V. Méot and P. Morel, Phys.Rev.C76, 044611 (2007). (*) G. Gosselin, V. Méot and P. Morel, Phys.Rev.C70, 064603 (2004). (*) P.Morel, V.Méot, G.Gosselin, D.Gogny and W.Younes, Phys.Rev.A69, 063414 (2004). nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  13. 26.27 keV 5/2- 630ps 1.56 keV 1/2- 81ns(*) 3/2- g.s. 0 keV 201Hg Nuclear excitations in plasmas Two level model Photon+NEEC/IC+NEET/BIC (thermodynamical equilibrium) Lifetime of first 201Hgm 201Hgm Future: inclusion of inelastic electron scattering (*) V.Méot, J.Aupiais, P.Morel, G.Gosselin, F.Gobet, J.N.Scheurer and M.Tarisien, Phys. Rev. C75, 064306 (2007). nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  14. Future • Variational multiparticle-multihole configuration mixing method Link with RPA Study of light nuclei- PhD proposal Test and possible re-fit of Gogny interaction (D2) • Spatial structure ofCooper pairs Generalization to deformed nuclei + pair transfer • Nuclear excitations in plasmas Inclusion of inelastic electron scattering nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  15. Description of correlations in mean field and beyond mean field methods Spatial structure of Cooper pairs in HFB approach Κ2(R,r) in Sn isotopes and Parity mixing effect Shell effects + Parity mixing effects nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

  16. Description of correlations in mean field and beyond mean field methods Spatial structure of Cooper pairs in HFB approach Probability Distribution Future study: Generalization to deformed nuclei where the parity mixing is expected to be stronger + nucleon pair transfer nathalie.pillet@cea.fr Jeunots 2008, February 4-6 (2008), Saclay

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